Continuity mistake: When Alex goes home in the night, he turns on his cassette player, takes out a cassette from the player, then after a few seconds a closeup is shown of the slot with a cassette inside that he removes again. (00:18:25)
Continuity mistake: When Frank first pours the wine for Alex he fills it all the way to the top. The shot changes and he is still pouring the wine however the level of the glass has dropped to half full and he fills it up again.

Continuity mistake: When Alex is informed that he's being transferred to the Ludovico center, the governor's arms jump from his lap to under his chin, then back to his lap. (01:06:00)
Chosen answer: It's part of the "fun element" of the crime to get the victim to open the door themselves.
Captain Defenestrator